By B. S. Everitt (auth.)

ISBN-10: 9400955642

ISBN-13: 9789400955646

ISBN-10: 940108954X

ISBN-13: 9789401089548

Latent variable types are utilized in many components of the social and behavioural sciences, and the expanding availability of machine programs for becoming such versions is probably going to extend their reputation. This e-book makes an attempt to introduce such versions to utilized statisticians and study staff attracted to exploring the constitution of covari ance and correlation matrices by way of a small variety of unob servable constructs. The emphasis is at the useful program of the approaches instead of on distinct dialogue in their mathe matical and statistical homes. it truly is assumed that the reader is aware the main widespread statistical options and strategies, really regression, and likewise has a good wisdom of matrix algebra. My thank you are because of my colleagues Dr David Hand and Dr Graham Dunn for useful reviews at the booklet, to Mrs Bertha Lakey for her cautious typing of a tricky manuscript and to Peter Cuttance for tips with the LlSREL package deal. moreover the textual content truly owes very much to the paintings on structural equation versions released by means of Karl Joreskog, Dag Sorbom, Peter Bentler, Michael Browne and others.

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**Extra resources for An Introduction to Latent Variable Models**

**Example text**

By shifting emphasis on the weighted average a more highly oblique positioning may be obtained, at the discretion of the investigator. Promax (Hendrickson and White, 1964) is a computationally efficient method which adjusts axes from an initial orthogonal position by attempting to further polarize the loadings. Harris and Kaiser (1964) give a set of methods, called orthoblique, which are invariant under rescaling of the axes. The question of whether orthogonal or oblique axes are more satisfactory can only really be answered on a case-tocase basis; the main question that the investigator needs to consider is whether or not the simplification in the factor loadings achieved, perhaps by having oblique axes, is offset by the added complexity introduced by their correlations.

In other words it is thought that three latent variables may account for the observed correlations between the eight tests, the first latent variable being indicated by tests 1 and 2, the second by variables 3-6 and the third by variables 7 and 8. It is also thought appropriate to include in the model a possible correlation between the second and third latent variables since these both contain variables which are tests of divergent thinking. The proposed model is illustrated by the path diagram of Fig.

However, this completely general approach is unlikely to be particularly helpful in encouraging the routine application of these techniques and, consequently, a number of less general, but practically more useful, approaches have been described. 2) where F is of order (Pj-1 x p), with Po = p, P is symmetric of order Pro Each element of Fj , or in some cases Fj- 1, and each element of P, or again in some cases p- 1, is a prescribed function of the t fundamental parameters in O. ) By specifying particular forms for the matrices Fj and P, this formulation allows a large number of models to be specified comparatively simply, and a computer program, COSAN (Covariance Structure Analysis), is available which allows estimation of the parameters using any of the three discrepancy functions described in Chapter 1.

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